A recursive formulation for the tesseral disturbing function in equinoctial variables
Abstract
This paper gives a compact expression for the potential in terms of nonsingular elements. Two fundamental expansions are developed and used. The first gives the spherical harmonics as a Fourier series in the orbital true longitude. The coefficients are similar to the Jacobi polynomials. The second expansion gives the products (r/a) to the nth exp (jmL) as a Fourier series in the mean longitude. The coefficients are similar to Hansen coefficients. Recursive formulas for these special functions are used to construct an efficient scheme for the numerical evaluation of the potential. Newcomb operators are also used. The resonant potential for a 14revolutionperday orbit is considered in detail.
 Publication:

AIAA and AAS, Astrodynamics Conference
 Pub Date:
 August 1976
 Bibcode:
 1976aaas.confS....C
 Keywords:

 Disturbing Functions;
 Equinoxes;
 Orbit Perturbation;
 Recursive Functions;
 Satellite Orbits;
 Tesseral Harmonics;
 Fourier Series;
 Operators (Mathematics);
 Orbital Mechanics;
 Polynomials;
 Spherical Harmonics;
 Astrodynamics